Correct Answer - C
Let `l=int_(0)^(pi//4)(4sin2theta d theta)/(sin^(4)theta+cos^(4)theta)=4int_(0)^(pi//4)(2sin theta cos theta d theta)/(sin^(4)theta+cos^(4)theta)`
`=4int_(0)^(pi//4)(2tan theta^(2)theta d theta)/(tan^(4)theta+1)`
Put `tan^(2) theta= t rArr 2 tan theta" "theta d theta=dt`
`therefore" "l=4int_(0)^(1)(dt)/(t^(2)+1)=4[tan^(-1)t]_(0)^(1)`
`=4[(pi)/(4)-0]=pi`
